Problem 4-65 Consider the uniformly loaded simply supported steel beam with an overhang as shown. The second-area moment of the beam is / 0.05 in. Using the singularity function method = determine the deflection equations of the beam. Plot the deflections. w = 100 lbf/in 10 in ДВ 4 in C

The cantilever beam ACB shown in the figure supports a uniform load of intensity q throughout its length. The beam has moments of inertia I2and IYin parts AC and CB, respectively. Using the method of superposition, determine the deflection SBat the free end due to the uniform load. Determine the ratio r of the deflection 6Bto the deflection 3Xat the free end of a prismatic cantilever with moment of inertia /] carrying the same load. Plot a graph of the deflection ratio r versus the ratio 12 //t of the moments of inertia. (Let 7, tlxvary from I to 5.)

-6 Calculate the maximum deflection of a uniformly loaded simple beam if the span length L = 2.0 m, the intensity of the uniform load q = 2.0 kN/m, and the maximum bending stress = 60 MPa, The cross section of the beam is square, and the material is aluminum having modulus of elasticity E = 70 GPa. (Use the formulas of Example 9-1.)

-6 A cantilever beam .4B is subjected to a parabolically valying load of intensity q(x)=q0(L2x2)/L2 where q0is the maximum intensity of the load (see figure). Derive the equation of the deflection curve, and then determine the deflection Band angle of rotation Bat the free end. Use the fourth-order differential equation of the deflection curve (the load equation).

A simple beam with an overhang is subjected to d point load P = 6kN. If the maximum allowable deflect ion at point C is 0.5 mm, select the lightest W360 section from Table F-l{b) that can be used for the beam. Assume that L = 3 m and ignore the distributed weight of the beam.

-3 The deflection curve for a simple beam AB (see figure) is given by v=q0x360LEI(7L410L2x2+3x4) Describe the load acting on the beam.

Beam ABC is loaded by a uniform load q and point load P at joint C. Using the method of superposition, calculate the deflection at joint C. Assume that L = 4 m, a =2ra, q = 15 kN/m, P = 7.5 kN, £ = 200 GPa, and / = 70.8 X 106 mm4.

Obtain a formula for the ratio c/maxof the deflection at the midpoint to the maximum deflection for a simple beam supporting a concentrated load P (see figure). From the formula, plot a graph of c/max versus the ratio a/L that defines the position of the load (0.5 < a/L < ) What conclusion do you draw from the graph? (Use the formulas of Example 9-3.)

A beam rests on supports at A and B and is loaded by a distributed load with intensity q as shown. A small gap exists between the unloaded beam and the support at C. Assume that span length L = 40 in. and flexural rigidity of the beam EI = 04 x 109lb-in2. Plot a graph of the bending moment at B as a function of the load intensity q. Hint: See Example 9-9 for guidance on computing the deflection at C.

Compound beam ABC is loaded by point load P = 1.5 kips at distance 2aB from point A and a triangularly distributed load on segment BC with peak intensity qü= 0.5 kips/ft. If length a = 5 ft and length/) = 10 ft, find the deflection at B and rotation at A. Assume that £ = 29,000 ksi and / = 53.8 in4.